6.1 How Many Solutions - Systems of Equations Quick Check

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What does it mean if a system of equations has no solutions?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The lines representing the equations are the same line, overlapping completely.

Front

How can you determine the number of solutions in a system of equations?

Back

By graphing the equations and observing the intersection points.

Front

What is the graphical representation of a system with one solution?

Back

Two lines intersecting at a single point.

Front

What is the graphical representation of a system with no solutions?

Back

Two parallel lines that do not intersect.

Front

What is the graphical representation of a system with infinitely many solutions?

Back

Two identical lines that overlap completely.

Front

If two equations are identical, how many solutions do they have?

Back

Infinitely many solutions.

Front

If two lines intersect at a point (x,y), what does that indicate?

Back

The values of x and y are the solution to the system of equations.